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Topic: Three Computers (Read 1074 times) |
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DP
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Three Computers
« on: Aug 4th, 2003, 9:09am » |
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There are 3 computers on sale in a hardware store - made in Japan, China and Russia. They all look exactly the same, with the only difference: the Japanese computer replies to any "yes/no" question with a true answer, the Chinese one - with a false answer, and the Russian one - either with a true or false answer randomly.
No one in a store (except for computers themselves, possessing the unlimited knowledge, of course) knows which computer is which.
You want to avoid the unpredictable Russian computer, and buy a "consistent" computer, no matter if it is Japanese or Chinese.
You are allowed to ask only one question to only one computer of your choise before deciding which one to buy.
Can you buy what you want, and if yes, how?
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prince
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Re: Three Computers
« Reply #1 on: Aug 4th, 2003, 3:56pm » |
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Assuming 1.) you may only ask a yes or no question and 2.) the "computer of your choise" is not identifiable by you, then the first key is:
ask your question to a computer that you will not buy. That way, if you ask the Russian, whose response is unpredictable, you are guaranteed to pick a "consistent" computer, whatever answer is given.
Call the computers A, B, and C
Ask a question of A, and pick either B or C
Then the only trouble is finding a question that:
gets the same response from both the Japanese and Chinese computer. So far, all I have is the cumbersome "If I ask the other non-Russian computer in the room 'Is computer B Russian?' what would it say?". Both Chinese and Japanese would answer 'no' if computer B is Russian, in which case, I pick C. If the answer is 'yes', then B is not Russian, so buy that one. Again, if I end up asking the Russian, it doesn't matter what the answer is, because either B or C would be "consistent".
I'm sure there is a less cumbersome question, but this should work.
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Icarus
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Re: Three Computers
« Reply #2 on: Aug 4th, 2003, 5:02pm » |
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A slightly less cumbersome approach is to ask of A "If I were to ask you 'Is B the Russian computer', would you answer 'yes'? If the answer is yes, buy C, otherwise buy B. I doubt you could do much better, as a meta-question is required to cancel out whether or not this is a lying computer.
Much better though would be to do your shopping at a store that doesn't remove the labels!
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James Fingas
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Re: Three Computers
« Reply #3 on: Aug 5th, 2003, 11:02am » |
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Here's a good question I've proposed for a similar problem (sorry, can't remember which one): Does computer #2 give correct answers more often than computer #3? Ask it of computer #1. If the answer is "no", buy computer #2. If the answer is "yes" buy computer #3.
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wowbagger
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Re: Three Computers
« Reply #4 on: Sep 23rd, 2003, 5:14am » |
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on Aug 4th, 2003, 9:09am, DP wrote:| There are 3 computers on sale in a hardware store - made in Japan, China and Russia. They all look exactly the same, with the only difference: the Japanese computer replies to any "yes/no" question with a true answer, the Chinese one - with a false answer, and the Russian one - either with a true or false answer randomly. |
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On behalf of a close friend of mine, I have to strongly object to the notion propagated herewith. Namely, that Russians, er, I mean Russian computers are unpredictable to such extreme an extent. Based upon personal experience, I can assure you that Russians are very often quite predictable,*which carries over naturally to the computers they construct.
* At least in being unpredictable.
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